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Inverted effective SUSY with combined Z' and gravity mediation, and muon anomalous magnetic moment

Effective supersymmetry(SUSY) where stop is the lightest squark may run into a two-loop tachyonic problem in some Z' mediation models. In addition, a large A term or/and a large stop mass are needed to have about a 126 GeV Higgs boson with three families of quarks and leptons. Thus, we suggest an inverted effective SUSY(IeffSUSY) where stop mass is larger compared to those of the first two families. In this case, it is possible to have a significant correction to the anomalous magnetic moment of muon. A three family IeffSUSY in a Z' mediation scenario is explicitly studied with the Z' quantum number related to B-L. Here, we adopt both the Z' mediation and gravity mediation where the Z' mediation is the dominant one for stop, while the gravity mediation is the dominant one for the muonic leptons and Higgs multiplets. We present a numerical study based on a specific anomaly free model, and show the existence of the parameter region where all the phenomenological conditions are satisfied.